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Three Questions

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Implicit Differentiation:Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
    x2/3 + y2/3 = 4 at (-3*31/2,1)


    2. Relevant equations
    ??? None?


    3. The attempt at a solution
    2/3 * x-1/3 + 2/3y-1/3*y' = 0
    then after a few steps of switching the sides of the variables

    y' = (-2x1/3)/ 2/3*y-1/3

    The part that I'm just confused on is putting x into the variables, especially since we're not suppose to use calculators, any help?
     
  2. jcsd
  3. Oct 12, 2009 #2

    Dick

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    3*3^(1/2)=3^(3/2). Does that help you simplify the x part?
     
  4. Oct 12, 2009 #3
    I think I got it, does the slope end up being -3*31/2??? Otherwise I did it incorrectly :P
     
  5. Oct 12, 2009 #4

    Dick

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    Yes, I think it does. It always helps to show your work when asking question like this.
     
  6. Oct 14, 2009 #5
    Wait wait wait, okay, when I plug in x..... how can I plug in a negative number into that....? -3^3/2 into x^- 1/3?????
     
  7. Oct 14, 2009 #6

    Dick

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    x^(-1/3) is one over the cube root of x. There isn't any problem with taking the cube roots of negative numbers.
     
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